Simplify/Condense 4 natural log of x+7 natural log of y-3 natural log of z

$4 \ln (x) + 7 \ln (y) - 3 \ln (z)$

Step 1

Simplify each term.

Simplify $4 \ln (x)$ by moving $4$ inside the logarithm.

$\ln (x^{4}) + 7 \ln (y) - 3 \ln (z)$

Simplify $7 \ln (y)$ by moving $7$ inside the logarithm.

$\ln (x^{4}) + \ln (y^{7}) - 3 \ln (z)$

Simplify $- 3 \ln (z)$ by moving $3$ inside the logarithm.

$\ln (x^{4}) + \ln (y^{7}) - \ln (z^{3})$

Step 2

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\ln (x^{4} y^{7}) - \ln (z^{3})$

Step 3

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$\ln (\frac{x^{4} y^{7}}{z^{3}})$